
We train CBMs on all 3 datasets using different training strategies - sequential and joint proposed by [1]} and hybrid as previously discussed with hyperparameters mentioned in Appendix. We train the respective models for CUB and OAI datasets based on the hyperparameters mentioned in [1]} as well as train hybrid models on both datasets to compare with standard models. In addition, we also train robust models using RCL (Algorithm REF  (Appendix)) utilizing both joint and hybrid training paradigms. The task errors for C-MNIST and CUB are classification error while for OAI, task error is Root Mean Square Error (RMSE) as the prediction label is a continuous variable. Concept error for C-MNIST and CUB is 0-1 error (binary concepts), while for OAI, concept error is RMSE (concepts are continuous variables). The benchmark results are reported in Table REF . As expected, performance of hybrid models lie between joint and standard models in task and concept performance. Usage of all 3 training paradigms presents a trade-off between task and concept performance depending on use-case. For eg., in high-risk settings, where concept accuracy is paramount (e.g. medical diagnosis), sequential can be utilized. Whereas tasks where small errors in concepts can be tolerated but prediction performance is important, joint can be utilized. Hybrid paradigm provides a good trade-off between both sequential and joint paradigms.
